Digital art has been around for ages, mostly lurking in dark, often politically radical ghettos of the internet, only occasionally surfacing in a more accessible form. But now, suddenly, it’s everywhere — in galleries and online, with whole exhibitions dedicated to its magic and digital curators sharing its joys.

Which is good news for the generation of digital natives who are making this new art world their own, adopting the internet and its resources as their language and affordable technology for their tools. These artists don’t confine themselves to computer screens, though — they’re as happy expressing themselves in the virtual realm as they are in “meatspace” (the real world).

Innovations come thick and fast. Even the term “post-internet art”, for that which is created with the internet’s resources, is already out of date. We are, say the vanguard, in the era of the “New Aesthetic”.

Institutions can no longer ignore these developments and seem to be enjoying playing catch-up. Today the Barbican Centre opens Digital Revolution, looking at the seismic ruptures shaking up design, film, music and video games, as well as art. The ICA’s current show, Journal, features an internet-art commission from Charlotte Prodger and Isla Leaver-Yap, and the Chisenhale Gallery’s autumn exhibition is Ed Fornieles, whose past projects include a “Facebook sitcom” and Bootyshake, created out of recycled webcam footage of dancing women.

Digital artists must be delighted to be taking pride of place in galleries, but an online platform is arguably more important. Last month, in a joint venture, the BBC and Arts Council relaunched The Space, an online platform for digital art commissions and collaborations which first appeared as part of the Cultural Olympiad. The Space has just collaborated on commissioning art body Artangel’s first fully digital project, the beautiful Jersualem, based on the 1966 World Cup, by Paul Pfeiffer. The Arts Council is also funding Opening Times, a not-for-profit digital art site hosting residencies and research commissions.

So the mainstream art world is suddenly awash with art made for or by computers. But what is it that the artists are making? The most obvious trend highlighted by the Barbican exhibition in this new era is for interaction with the physical world. The show is dominated by highly interactive works that produce experiences rather than present objects. They cross discipline, too, from installation art to design, architecture and gaming. Unashamedly entertaining, they’re made by artists who are as likely to do a music video or create festival spectaculars as they are to appear in a gallery.

Take Chris Milk’s The Treachery of Sanctuary (2012), a digital play on shadow puppetry, one of several works in the Barbican which resulted from creative hacking of Microsoft’s hands-free gaming console, Kinect. Here, you stand before three vast screens, in which your body appears as a black silhouette. In one screen your movements trigger your body to dissolve into hundreds of screeching birds, in the next, the birds drop down and eat you, limb from limb. In the last, you’re reborn as a bird yourself: throw out an arm and it develops a vast eagle’s wing.

Another example of this physical-digital mix, Umbrellium’s Assemblance, is in The Pit, the Barbican’s small theatre venue (the show seeps into all corners of the building). It’s an apt setting because, like so many of these interactive works, it makes you a performer. Beams of light, made smoky with dry ice, project lines, dots and bars onto the floor in an otherwise pitch-black space. You then manipulate the beams to make drawings on the floor. Trust me, it’s fun.

Elsewhere in the show, Universal Everything’s Together allows visitors to create animations on a special app, which then become part of the video wall in the Barbican’s Silk Street entrance hall. Together was co-produced with The Space, which also collaborated on a 24-hour hackathon at Tate Modern recently.

Where many of the multimedia installations in the Barbican are entertaining and celebratory, online art is similarly immersive but also often more ambiguous, complex and more critical, exploiting while also questioning the internet’s resources.

Just as conceptual art often makes subversive reference to the gallery experience (they call it “institutional critique” but you needn’t bother with that), so online art critiques web space. The first project commissioned by Ben Vickers, the Serpentine’s first digital art curator, has been unleashed on the gallery’s website. AGNES, created by Belgian-American artist Cécile B Evans, is a “spambot” — a generator of spam, though this one with a difference who visitors can make friends with. Initially, she comes across as a candy-voiced, friendly character, welcoming you to her brightly coloured and patterned site but soon she’s asking creepily personal questions about whether you have children, for instance, and why.

Even more spookily, AGNES collects data, such as your mother’s name, that of your “greatest childhood enemy” or of “someone you wanted to kiss but never did” — the kind of questions that make you wonder what she’ll do with your personal information. She also produces web pages about internet security systems that reinforce your paranoia and make you question your behaviour in the social media-drenched online world.

Images and video footage found on the web, from movies to cute cats, also abound in AGNES’s world — it’s like a constantly shifting animated collage drawn from a vast online archive, always underlined by social and political commentary.

Evans’s work is genuinely original, and like much online art, it evolves with each visit, harnessing the qualities which distinguish the internet from meatspace. This kind of art feels like the future — so it’s just as well that galleries are at last ready to bring it to a wider audience.